Filter

ABSTRACT

Here disclosed is a parallel-resonance type band-pass filter, which is employed for mobile communications equipment such as a mobile phone. According to the filter, each resonator has a single capacitor and serially connected plural inductors both of which are formed on the surface or on an inner layer of a substrate. Electromagnetic coupling between the resonators is established through electromagnetic coupling between at least a pair of inductors—the inductors of the pair belong to respective resonators. The input and the output terminals are coupled with the respective resonators via the capacitor having a properly determined capacitance. With such a simple structure, the filter also can work as an impedance transformer, with the result that the mobile communications equipment will be much smaller.

FIELD OF THE INVENTION

[0001] The present invention relates to a filter typically employed inmobile communications equipment, such as a mobile phone.

BACKGROUND OF THE INVENTION

[0002] With the increasing use of a mobile phone and other mobilecommunications in recent years, a demand for more compact andinexpensive mobile communications equipment including mobile phones hasnow been growing. To serve the demands, it is essential to form eachelectric circuit as a component of such equipment to be smaller andlower in cost. It has been difficult, however, to structure aradio-frequency circuit section compact because of a filter that is hardto be integrated into one chip. Therefore, miniaturization andintegration of each circuit component in a radio-frequency circuitsection will be a key factor in structuring the equipment compact andinexpensive.

[0003]FIG. 6 is a block diagram depicting a typical radio-frequencycircuit section of prior-art mobile communications equipment. In FIG. 6,an radio frequency transmission signal generated at IC 601 is fed intoband-pass filter 603 via impedance transformer 602. Impedancetransformer 602 is responsible for matching the impedance of IC 601 tothat of transmission band-pass filter 603. After passing throughband-pass filter 603, the radio frequency transmission signal ispower-amplified by amplifier 604. After that, the signal goes throughduplexer 605 then radiates from antenna 607. Impedance transformer 602above may be the type that splits the signal path into two branchesaccording to the specifications of IC 601.

[0004] In either case, impedance transformer 602 and band-pass filter603 are separately structured as an independent circuit component,taking up too much space in the circuit. The structural limitations havetherefore been an obstacle to more downsized and inexpensive equipmentusing such components.

SUMMARY OF THE INVENTION

[0005] The present invention addresses the problem above. It istherefore an object of the present invention to provide a downsizedfilter by integrating a band-pass filter with an impedance transformerinto a simple structure with the help of electromagnetic couplingbetween parallel resonators.

[0006] The filter disclosed in the present invention is aparallel-resonance type band-pass filter, which includes a substrate, afirst resonator, and a second resonator.

[0007] The first resonator includes a capacitor and a plurality ofconnected-in-series inductors, both of which are formed on the surfaceor an inner layer of a substrate.

[0008] Similarly, the second resonator includes a capacitor and aplurality of connected-in-series inductors, both of which are formed onthe surface or an inner layer of a substrate.

[0009] The electromagnetic coupling between the first and secondresonators is established by at least the electromagnetic couplingbetween one of the inductors of the first resonator and one of theinductors of the second resonator.

[0010] The present invention has various aspects described below:

[0011] (1) inductors for each resonator may be three or moreconnected-in-series inductors. In this case, flexibility in designing aresonator will be increased.

[0012] (2) a capacitor for each resonator may be an inter-digital typecapacitor. This will realize a capacitor formed on a single layersubstrate, allowing the filter to have a low profile.

[0013] (3) employing a balanced-type terminal for at least one of theinput terminal and the output terminal, and connecting each terminal ofthe balanced-type terminal with a resonator via a capacitor. This willrealize a balanced-type, 2-stage parallel-resonance type band-bassfilter

[0014] (4) grounding the middle point of the connected inductors in theresonator will eliminate unstable operations occurred at the groundedposition in frequencies of the microwave-frequency band or higher.

[0015] (5) making a difference between the input impedance and theoutput impedance of a filter allows the filter to also serve as animpedance transformer as well.

[0016] (6) employing a dielectric material for the substrate willrealize a smaller filter.

[0017] (7) employing a semiconductor wafer for the substrate allows afilter not only to be compact, but also to integrate with othersemiconductor parts onto an IC chip.

[0018] (8) aforementioned semiconductor may be: i)silicon, ii) galliumarsenide, iii) silicon-germanium, iv) indium phosphide, or v) a compoundhaving any one of elements above i) through iv) as a major constituent.Such formed filter will be able to exploit each own advantage accordingto a use.

[0019] (9) aforementioned inductors may be formed by anintaglio-printing technique or a thin-film forming technique to form thefilter compact.

[0020] (10) aforementioned capacitors may be formed by a thin film-, ora thick film-forming techniques to form the filter compact.

[0021] (1) the filter electrodes may be made of: i) copper, ii) silver,or iii) a metal compound having one of copper and silver as a majorconstituent. This contributes to a strength-increased substrate, orsimplified manufacturing steps.

[0022] With such structures described above, according to the presentinvention, it is possible to form a filter not only determining thedegree of coupling with flexibility between the resonators, but alsodetermining an input impedance so as to be different from an outputimpedance. This advantage realizes a band-pass filter that doubles as animpedance transformer, shrinking the physical size of mobilecommunications equipment using the filter.

BRIEF DESCRIPTION OF THE DRAWINGS

[0023]FIG. 1 is a circuit diagram of the filter in accordance with afirst preferred embodiment of the present invention.

[0024]FIG. 2 is another circuit diagram of the filter in accordance withthe first preferred embodiment.

[0025]FIG. 3 is a circuit diagram of the filter in accordance with asecond preferred embodiment of the present invention.

[0026]FIG. 4 is a circuit diagram of the filter in accordance with athird preferred embodiment of the present invention.

[0027]FIG. 5 is a circuit diagram of the filter in accordance with afourth preferred embodiment of the present invention.

[0028]FIG. 6 is a circuit block diagram of mobile communicationsequipment using a prior-art filter.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0029] The preferred embodiments of the present invention are describedhereinafter with reference to the accompanying drawings.

[0030] First Preferred Embodiment

[0031] In the filter of the embodiment, as shown in FIG. 1, resonator111 is electromagnetically coupled with resonator 112 through inductors105 and 110. Resonator 111 is formed of a parallel-resonance circuithaving two connected-in-series inductors 103, 105; and capacitor 104placed across the inductors. Similarly, resonator 112 is formed of aparallel-resonance circuit having two connected-in-series inductors 108,110; and capacitor 109 placed across the inductors.

[0032] As shown in FIG. 1, inductor 103 and capacitor 104 are connectedto capacitor 102, which is connected to input terminal 101. On the otherhand, inductor 108 and capacitor 109 are connected to capacitor 107,which is connected to output terminal 106. Each connecting point ofcapacitor 104 and inductor 105, and of capacitor 109 and inductor 110 isgrounded.

[0033] Here will be described how such structured filter works. Inresonator 111, capacitor 104 has a given capacitance. Resonancefrequency f₀ of resonator 111 is derived from the capacitance ofcapacitor 104 and a combined inductance of inductors 103, 105. Thecapacitance of capacitor 102 is determined according to J-inverter ongenerator side based on a filter-designing theory—for detailedinformation on J-inverter, for example, see “Microwave Filters,Impedance-Matching Networks, and Coupling Structures” written by G. L.Matthaei, L. Young, and E. M. Jones, McGraw-Hill New York, 1964.

[0034] The capacitance of capacitor 104 is corrected on the basis of theJ-inverter. Similarly, in resonator 112, capacitor 109 has a givencapacitance. According to the capacitance of capacitor 109, a combinedinductance of inductors 108 and 110 is determined so as to be equal toresonance frequency f₀ of resonator 112. The capacitance of capacitor107 is determined according to J-inverter on load side, and according towhich, the capacitance of capacitor 109 is corrected.

[0035] The physical distance between inductors 105 and 110 is related tomutual inductance “M”—the value of mutual inductance “M” determines thepositional relation between the inductors. Mutual inductance “M” isgiven by the equations below:

k−J/b,

[0036] then,

M=k·[L ₁₀₅ ·L ₁₁₀]^(½)

[0037] Where, J indicates a value of J-inverter between the resonators;b indicates a susceptance slope parameter of resonator 111 or 112; kindicates a degree of coupling between resonators 111 and 112; L₁₀₅indicates the inductance of inductor 105; and L₁₁₀ indicates theinductance of inductor 110.

[0038] The equation above is expressed as below, using the correctedcircuit component values (indicated by each symbolic letter with “”′)according to the J-inverter:

M=k′·[L′ ₁₀₅ ·L′ ₁₁₀]^(½)

[0039] The degree of coupling (indicated by k) can take any given valueas long as the equations below are satisfied.

k′=n·k,

L′ ₁₀₅ =L ₁₀₅ /n,

L′ ₁₁₀ =L ₁₁₀ /n,

L′ ₁₀₃ +L′ ₁₀₅ =L ₁₀₃ +L ₁₀₅=constant,

L′ ₁₀₈ +L′ ₁₁₀ =L ₁₀₈ +L ₁₁₀=constant,

[0040] where, n takes a proper real number, and L₁₀₃ and L₁₀₈ indicatethe each inductance of inductors 103 and 108.

[0041] Such determined k brings greater design flexibility not only informing the inductors, but also in determining the positional relationbetween inductors 105 and 110 in the circuit.

[0042] The circuit with the structure above functions as a 2-stageparallel-resonance type band-pass filter having input terminal 101 andoutput terminal 106, thereby realizing a smaller filter.

[0043] Although two inductors are employed for the resonator of theembodiment, it is not limited to this: the resonator may include threeor more inductors, as shown in FIG. 2. Such a structure advantageouslyincreases flexibility in laying out the circuit components on asubstrate.

[0044] Besides, the capacitor of the embodiment may be an inter-digitaltype capacitor. In this case, it is possible to form capacitorelectrodes into a single layer, allowing the entire filter circuit to beformed into a single layer.

[0045] Therefore, with such structured filter described in theembodiment, mobile communications equipment becomes much smaller.

[0046] Second Preferred Embodiment

[0047]FIG. 3 is a block diagram of the filter in accordance with thesecond preferred embodiment of the present invention. According to theembodiment, circuit components forming a filter are arranged on the topsurface of dielectric substrate 301. At least three terminalelectrodes—terminals 306 a, 306 b, and 306 c—for an input terminal, anoutput terminal, and a grounding section, as shown in FIG. 3, are formedon the side surfaces of substrate 301. Between the two resonators inFIG. 3, electromagnetic coupling is established through inductorelectrodes 305 and 310. The first resonator forms a parallel-resonancecircuit, including connected-in-series two inductor electrodes 303, 305;and capacitor electrode 304 placed across the inductors—from the figure,it will be understood that electrode 304 contains electrodes 304 a and304 b. Like the first resonator, the second resonator forms a parallelresonance circuit, including connected-in-series two inductor electrodes308, 310; and capacitor electrode 307 placed across the inductors.Inductor electrode 303 and capacitor electrode 304, as shown in FIG. 3,are connected to capacitor electrode 302, which is to be connected withterminal electrode 306 a. Similarly, inductor electrode 308 andcapacitor electrode 307 are connected to capacitor electrode 309, whichis to be connected with terminal electrode 306 b. The connecting pointsof capacitor electrode 304 and inductor electrode 305, and of capacitorelectrode 307 and inductor electrode 310 are both connected withterminal electrode 306 c. Terminal electrode 306 c is connected togrounding electrode 313 formed on the rear surface of substrate 301.

[0048] Now will be described how such structured filter works. Accordingto the filter of the embodiment, as described above, the capacitorelectrodes operate in pairs to form an inter-digital type capacitor. Onthe other hand, the inductor electrodes work with an inductanceproportional to a characteristic impedance of a transmission path, whichis determined by the dielectric constant, the thickness, the shape andthe dimensions of the electrode of dielectric substrate 301. That is,the filter has the structure the same as that of the first preferredembodiment, working as a 2-stage parallel-resonance type band-passfilter. As an additional plus, the circuit components of the filter canbe formed by an electrode pattern with extra-fine lines, therebyrealizing a compact filter with an easily formed circuit configuration.

[0049] Although the electrode of the embodiment is formed on the surfaceof the dielectric substrate, it can be formed on an inner layer of amulti-layered dielectric substrate. In this case, the capacitor can bestructured in a parallel-plate-type, offering an advantage in that thecapacitor bears a greater capacitance. Besides, it is possible to formthe inductor into a spiral-type to be compact.

[0050] Now will be described substrate materials and manufacturingmethod of circuit components.

[0051] (1) Substrate materials

[0052] Although the electrode of the embodiment is formed on the surfaceof a dielectric substrate, it can be formed on or in a semiconductorwafer. In this case, the filter can be not only formed compact, but alsoformed, together with semiconductor parts including a transistor and adiode, into one IC chip.

[0053] When a semiconductor wafer is used for the substrate, instead ofdielectric materials, the semiconductor may be silicon or a compoundcontaining silicon as a major constituent. Such a general versatilesemiconductor material offers an advantage in realizing ageneral-purpose manufacturing process.

[0054] As another choice, the semiconductor may be gallium arsenide or acompound containing gallium arsenide as a major constituent. Such formedsubstrate allows a filter to easily integrate with amplifying andswitching circuits, or transistor and other parts, increasing the scaleof an integrated circuit.

[0055] As still another choice, the semiconductor may besilicon-germanium or a compound containing silicon-germanium as a majorconstituent. The material contributes to a cost-reduced filter.

[0056] As yet another choice, the semiconductor may be indium phosphideor a compound containing indium phosphide as a major constituent. Thematerial enables to easily form a filter that can work in themicrowave-frequency band or higher.

[0057] (2) Manufacturing method of the circuit components

[0058] Inductors and capacitors, which are the circuit components of theembodiment, can be formed by a thick-film forming technique. In thiscase, a screen-printing technique can be employed to simplify themanufacturing process.

[0059] As another choice, the inductors and capacitors may be formed bya thin-film forming technique. In this case, an intaglio-printingtechnique can be employed. Using the technique has advantages in thatthe capacitor can be downsized, as well as the inductors-furthermore, amicro-capacitor can be produced as needed.

[0060] In addition, the inductors and capacitors of the embodiment canbe made of copper or a metal compound containing copper as a majorconstituent. In this case, the substrate of the component can bear highsintering temperature, thereby increasing mechanical strength ofsubstrate.

[0061] As another choice, the inductors and capacitors of the embodimentmay be made of silver or a metal compound containing silver as a majorconstituent. In this case, the substrate can be sintered together withthe inductors and capacitors, thereby simplifying the manufacturingprocess.

[0062] Therefore, with such structured filter described in theembodiment, mobile communications equipment becomes much smaller.

[0063] Third Preferred Embodiment

[0064]FIG. 4 is a circuit diagram of the filter according to the thirdpreferred embodiment of the present invention. In the filter of theembodiment, as shown in FIG. 4, resonators 416 and 417 areelectromagnetically coupled with each other through the electromagneticcoupling established between inductors 405 and 413, and betweeninductors 406 and 415. Resonator 416 forms a parallel-resonance circuit,including connected-in-series inductors 403, 405, 406, and 407; andcapacitor 404 placed across these inductors. Similarly, resonator 417forms a parallel-resonance circuit, including connected-in-seriesinductors 411, 413, 415, and 414; and capacitor 412 placed across theseinductors.

[0065] Resonator 416 is connected to input terminal 401 via capacitor402. To capacitor 402, inductor 403 and capacitor 404 of resonator 416are connected as shown in FIG. 4. On the other hand, resonator 417 isconnected, as shown in FIG. 4, to output terminal 408 via capacitors 409and 410. To capacitor 409, inductor 411 and capacitor 412 of resonator417, while to capacitor 410, inductor 414 and capacitor 412 areconnected. The connecting points of inductor 407 and capacitor 404 ofresonator 416, and of inductor 413 and inductor 415 of resonator 417 areboth grounded.

[0066] Now will be described hereinafter how such structured filterworks. Capacitor 404 has a given capacitance. Resonance frequency f₀ ofresonator 416 is derived from the capacitance of capacitor 404 and acombined inductance of inductors 403, 405, 406, and 407. The capacitanceof capacitor 402 is determined according to J-inverter on generator sidebased on a filter-designing theory. The capacitance of capacitor 404 iscorrected on the basis of the J-inverter. Similarly, capacitor 412 has agiven capacitance. According to the capacitance of capacitor 412, acombined inductance of inductors 411, 413, 414,and 415 is determined sothat the resonance frequency of resonator 417 is equal to f₀. Eachcapacitance of capacitors 409 and 410 is determined so as to take avalue doubled the value according to J-inverter on load side, and thecapacitance of capacitor 412 is corrected according to the value ofJ-inverter. The physical distance between inductors 405 and 413 isrelated to mutual inductance M₂₆: the value of mutual inductance M₂₆determines the positional relation between the inductors. Similarly, thephysical distance between inductors 406 and 415 is related to mutualinductance M₃₈, which determines the positional relation between theinductors 406 and 415. These Mutual inductances M₂₆ and M₃₈ are given bythe equations below:

k=J/b,

[0067] then,

M ₂₆ =k·[L ₄₀₅ ·L ₄₁₃]^(½,)

M ₃₈ =k·[L ₄₀₆ ·L ₄₁₅]^(½,)

[0068] Where, J indicates a value of J-inverter between the resonators;b indicates a susceptance slope parameter of resonator 416 or 417; kindicates a degree of coupling between resonators 416 and 417; L₄₀₅,L₄₀₆, L₄₁₃, and L₄₁₅ indicate the inductance of inductors 405, 406, 413,and 415, respectively.

[0069] Here, each inductance of the inductors above is determined so asto satisfy the equations below:

L ₄₀₃ =L ₄₀₇,

L ₄₀₅ =L ₄₀₆,

L ₄₁₁ =L ₄₁₄,

L ₄₁₃ =L ₄₁₅.

[0070] Where, L₄₀₃, L₄₀₇, L₄₁₁, and L₄₁₄ indicate the inductance ofinductors 403, 407, 411, and 414, respectively.

[0071] The equation above is expressed as below, using the correctedcircuit component values (indicated by each symbolic letter with“”′)according to the J-inverter:

M ₂₆ =k′·[L′ ₄₀₅ ·L′ ₄₁₃]^(½,)

M ₃₈ =k′·[L′ ₄₀₆ ·L′ ₄₁₅]^(½.)

[0072] The degree of coupling (indicated by k) can take any given valueas long as the equations below are satisfied.

k′n·k,

L′ ₄₀₅ =L ₄₀₅ /n,

L′ ₄₀₆ =L ₄₀₆ /n,

L′ ₄₁₃ =L ₄₁₃ /n,

L′ ₄₁₅ =L ₄₁₅ /n,

L′ ₄₀₃ +L′ ₄₀₅ +L′ ₄₀₆ +L′ ₄₀₇ =L ₄₀₃ +L ₄₀₅ +L ₄₀₆ +L ₄₀₇=constant,

L′ ₄₁₁ +L′ ₄₁₃ +L′ ₄₁₄ +L′ ₄₁₅ =L ₄₁₁ +L ₄₁₃ +L ₄₁₄ +L ₄₁₅=constant,

[0073] where, n takes a proper real number.

[0074] Such determined k brings greater design flexibility not only informing the inductors, but also in determining the positional relationbetween inductors 405 and 413, and between inductors 406 and 415.Therefore, It becomes possible to form the circuit components of thefilter by an extra fine lined-electrode pattern, with the componentpositioned closer to each other.

[0075] Such structured filter has input terminal 401 and output terminal408, with the side of output terminal 408 formed into a balancedtype—the filter functions as a 2-stage parallel-resonance type band-passfilter. As an additional plus, the circuit components of the filter canbe formed by an extra fine lined-electrode pattern, thereby realizing acompact filter with an easily formed circuit configuration.

[0076] The connecting point of inductor 413 and inductor 415 is notnecessarily grounded, although it is done in the embodiment. Grounding,however, conveniently eliminates an unstable operation at the connectingpoint in the microwave-frequency band or higher.

[0077] While the dielectric substrate, and the conductor patternsdescribed in the embodiment can be formed by various methods, it will beunderstood that the present invention is not limited to any one of them.

[0078] According to the embodiment, as described above, with the shrunkfilter, mobile communications equipment becomes much smaller.

[0079] Fourth Preferred Embodiment

[0080]FIG. 5 is a circuit diagram of the filter according to the fourthpreferred embodiment of the present invention. As the filter of theembodiment is formed basically the same as that described in the firstpreferred embodiment, those parts corresponding to the components in thefirst preferred embodiment will be identified with the same numbers, anddetailed explanations thereof will be omitted. In FIG. 5, capacitor 518connects terminal 106 to second resonator 520, and capacitor 519 is acircuit component of the second resonator 520. Each capacitance of thecapacitors is determined different from those in the first preferredembodiment.

[0081] Here will be described how such structured filter works. In thefilter of the embodiment shown in FIG. 5, the impedance on load side isdifferently determined from that on generator side. The value ofJ-inverter on load side is given by the equation below.

J=[(1/Z)·2π·ω·C/(g ₂ ·g ₃)]^(½)

[0082] where, ω indicates a bandwidth; C indicates the capacitance ofcapacitor 519 determined at any given value; and g₂, g₃ indicate thesecond and the third g-parameters, respectively, in the prototype filterof the filter circuit of the embodiment.

[0083] In the filter of the embodiment, as described above, theJ-inverter in the equation is so determined that load impedance “Z”takes a value different from that on generator side. The capacitance ofcapacitor 518 is determined according to such defined J-inverter havinga value of “J”. Also, substituting “J” into the equation describedabove, the corrected capacitance of capacitor 519 can be obtained.

[0084] The filter with the structure described above works as a filterhaving input impedance different from output impedance. In other words,the filter functions as a 2-stage parallel-resonance type band-passfilter, which doubles as an impedance transformer. Besides, as is thecase with the aforementioned embodiments, the circuit components of thefilter can be formed by an electrode pattern with extra-fine lines,thereby realizing a compact filter with an easily formed circuitconfiguration.

[0085] The idea—forming the filter to serve as an impedancetransformer—of the embodiment is also applicable to the third preferredembodiment. In this case, the filter works as a balanced-, 2-stageparallel-resonance-type band-pass filter, serving as an impedancetransformer. Moreover, the circuit components of the filter can beformed by extra fine lined-electrode patterns, thereby realizing acompact filter with an easily formed circuit configuration.

[0086] With the filter according to the present invention, as describedabove, it will be possible not only to determine with flexibility thedegree of coupling between the resonators, but also to determine theinput impedance so as to be different from the output impedance. Thisfact allows the band-pass filter to also behave as an impedancetransformer, and mobile communications equipment with such a compactfilter will shrink its physical size.

What is claimed is:
 1. A parallel-resonance type band-pass filtercomprising: a substrate; a first resonator including: i) a firstcapacitor; and ii) a first plurality of inductors connected in series,both of which are formed on a surface, or on an inner layer of thesubstrate; and a second resonator including: i) a second capacitor; andii) a second plurality of inductors connected in series, both of whichare formed on a surface, or on an inner layer of the substrate, whereinelectromagnetic coupling between the first resonator and the secondresonator is performed by at least electromagnetic coupling between oneof the first plurality of inductors and one of the second plurality ofinductors.
 2. The filter of claim 1, wherein the first resonator and thesecond resonator are respectively coupled with an input terminal and anoutput terminal of the filter via a capacitor.
 3. The filter of claim 1,wherein each number of the first plurality of inductors and the secondplurality of inductors is at least three.
 4. The filter of claim 1,wherein the first capacitor and the second capacitor are inter-digitaltype capacitors.
 5. The filter of claim 2, wherein the first capacitor,the second capacitor, and the capacitors which connect the inputterminal and the output terminal to the first resonator and the secondresonator respectively are inter-digital type capacitors.
 6. The filterof claim 2, wherein at least one of the input terminal and the outputterminal is a balanced-type terminal, and any one of the first resonatorand the second resonator, which is connected to the balanced-typeterminal, is connected to each terminal of the balanced-type terminalvia the capacitor.
 7. The filter of claim 6, wherein the capacitor whichis connected to the balanced-type terminal is an inter-digital typecapacitor.
 8. The filter of claim 1 or claim 2, wherein a middle pointof at least one of the first plurality of inductors and the secondplurality of inductors is grounded.
 9. The filter of claim 1 or claim 2,wherein the filter has an input impedance different from an outputimpedance.
 10. The filter of claim 1 or claim 2, wherein the substrateis made of a dielectric material.
 11. The filter of claim 1 or claim 2,wherein the substrate is made of a semiconductor wafer.
 12. The filterof claim 1 or claim 2, wherein the substrate is made of a semiconductorwafer, the semiconductor is any one of i) silicon, ii) gallium arsenide,iii) silicon-germanium, iv) indium phosphide, and v) a compound havingany one of the silicon, the gallium arsenide, the silicon-germanium, andthe indium phosphide, as a major constituent.
 13. The filter of claim 1,wherein the inductors structuring the first resonator and the secondresonator are formed by any one of an intaglio-printing technique and athin-film forming technique.
 14. The filter of claim 1 or claim 2,wherein the first capacitor and the second capacitor are formed by anyone of a thick-film forming technique and a thin-film forming technique.15. The filter of claim 2, wherein the first capacitor, the secondcapacitor, and the respective capacitors connecting the first and thesecond resonators to the input and the output terminals are formed byany one of a thick-film forming technique and a thin-film formingtechnique.
 16. The filter of claim 1 or claim 2, wherein an electrodeforming the filter are made any one of i) copper, ii) silver, and iii) ametal compound having one of the copper and the silver as a majorconstituent.